Title: Between quantum logic and concurrency
Citation: Proceedings 9th Workshop on Quantum Physics and Logic p. 65-75
Publisher: EPTCS
Publication Year: 2014
JRC N°: JRC73932
ISSN: 2075-2180
URI: http://publications.jrc.ec.europa.eu/repository/handle/JRC73932
DOI: 10.4204/EPTCS.158
Type: Articles in periodicals and books
Abstract: We start from two closure operators defined on the elements of a special kind of partially ordered sets. These are called causal nets, and are used to model histories of concurrent processes, recording occurrences of local states and of events. If every maximal chain (line) of the partially ordered set meets every maximal antichain (cut), then the two closure operators coincide, and generate complete orthomodular lattices. In this paper we recall that, for any closed set in this lattice, every line meets either it or its orthocomplement in the lattice, and show that to any line, a two-valued state on the lattice can be associated. Starting from this result, we delineate a logical language whose formulas are interpreted over closed sets of a causal net, where every line induces an assignment of truth values to formulas. The resulting logic is non-classical; we show that maximal antichains in a causal net are associated to Boolean (hence ``classical'') substructures of the overall quantum logic.
JRC Directorate:Space, Security and Migration

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